# Basis Point Calculator

Created by Rita Rain and Tibor Pal, PhD candidate
Reviewed by Bogna Szyk and Jack Bowater
Based on research by
Cipra, T. Financial and Insurance Formulas (2006)
Last updated: Mar 17, 2022

The basis point calculator will help you conveniently convert between basis points (BPS), percents, permilles, and decimal values. Just input one number, and the rest will be calculated for you automatically. In the text below, you will find what a basis point is, how to calculate it, and what it is used for.

## What is a basis point?

A basis point (often denoted as BP and pronounced as "bip" or "beep") is a unit of measurement frequently used in finance. It is equal to 1/100th of 1 percent, which is 1 permyriad. The concepts of percent, permille, permyriad, and basis point are related in the following manner:

1 percent 1% = 1/100

1 permille 1‰ = 1/1000

1 permyriad 1‱ = 1/10000

Our basis point calculator uses these equations to help you convert basis points to percents and permilles.

To know more about how percentage works, check out our percentage calculator.

## Why do we have basis points?

You may ask yourself why do we need to use basis points if they are the same as permyriads. Well, while these concepts are related, they are not exactly the same. The relation between a basis point and a permyriad is the same as between a percent and a percentage point. A basis point is equal to the value of a permyriad, but it is used when we speak about changes in percentage rates.

For example, let's say that in some country the unemployment rate in 2017 was 6%. By 2018, this value had changed to 16%. You may want to say that the value has increased by 10%, but it is not quite clear whether you mean that it changed from 6% to 6.6% (a relative value) or from 6% to 16% (an absolute value).

To avoid this confusion, you can say it has increased by 1000 BPS. Then we know that you mean the second scenario, that is the increment by points, not by a percentage of a percentage. In this way, basis points help to eliminate ambiguity when talking about rate changes.

If you are confused about rate changes, take a look at our percentage of a percentage calculator or the percentage difference calculator.

## How to convert basis points to percents?

The easiest way is to put a number into any field of the basis point calculator and let it do the math for you!

It's not, however too difficult to do it by hand, so if you want to convert:

1. Basis points to percents - divide the points by 100.
2. Percentage to basis points – multiply the rate by 100.

For example:

1. You read that: "The average rate for a 30-year fixed mortgage is 4.09 percent, an increase of 9 basis points since the same time last week." To know what the rate used to be, divide bps by 100:

9 / 100 = 0.09

Since it has increased, subtract the value from the current rate:

4.09 - 0.09 = 4

The average rate used to be 4%.

2. You want to say that Australia's central bank's benchmark interest rate decreased from 1.5% to 1.25%.

To express the percentage in basis points, calculate the difference and multiply it by 100:

1.5% - 1.25% = 0.25%

0.25 * 100 = 25

You can say that the interest rate decreased by 25 BPS.

## Where are basis points used?

Basis points are mainly used in finance to describe the percentage changes or to denote a difference between two interest rates, especially when the rate difference is less than 1 percent. Basis points are used for measuring yields, loans, treasury bonds, corporate bonds, interest rate derivatives, credit derivatives, and debt securities such as mortgage loans. They are the smallest unit of measurement for financial instruments, but don't underestimate them. They can be very significant, as in some situations small changes in rates can have substantial economic outcomes.

## FAQ

### What are basis points in mortgage?

A basis point in mortgage is a change equivalent to 0.01%. For example, if your mortgage was at 3.62%, and decreases by 15 basis points, it is now at 3.47%. An increase of a single basis point can be worth quite a lot. For example, your $500000 mortgage at 4.5% requires a monthly repayment of$2.406.76. An increase of 1 bps means you must now pay an additional $2.82 a month, which totals an additional$1016 in payment.

### Can basis points be negative?

Basis points can be negative, as they represent the change from one value to another, although you are more likely to say ‘a bond has decreased by 25 basis points’ than ‘a bond has increased by -25 basis points,’' despite these two statements having the same meaning.

### Why do we use basis points?

Basis points are used to remove any uncertainty when talking about percentage change. To say ‘my commission is usually 10%, but it increased by 10% last quarter’ is needlessly ambiguous; is your commission now 20%, or 11%? This is why we use basic points, so that we know when someone says a 100 basis point increase they mean an increase of 1%.

### How much is 40 basis points?

40 basis points is equivalent to 0.4% or 0.004 in decimal form. This is because 1 basis point is 0.01%. How much 40 basis points will be will depend on the initial value; for $300, 40 basis points would only be$1.20, while for $1 million, 40 basis points, is$4000.

3. Multiply the value for 1 basis point by how many basis points you earn from commission. We earn a 30 bps commission, so we earnt $45 on our sale. ### What is 50 basis points in decimal form? For a value of 1, 50 basis points is 0.005. The value of 50 basis point in decimal form will depend on the value you are talking about: 1. 50 basis points is equal to 0.5% of the value. 2. So we'd multiply the value by 0.5%. 3. This would give us the basis points in decimal form. So, for$97500, 50 basis points in decimal form will be $487.50, while for$700 it would be $3.50. Rita Rain and Tibor Pal, PhD candidate Decimal value Percent % Permille Basis points bps What is x bps of y? bps of$
equals
$1.5 bps of$65,000.00 equals $9.75 Example: a stock worth$65,000.00 has increased by 1.5 bps - this means its value has increased by 9.75, and the stock is now worth \$65,009.75.
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